Relativistic and charge-displacement self-channeling of intense ultrashort laser pulses in plasmas

Analytic theory of relativistic self-focusing for a Gaussian light beam entering a plasma: Renormalization-group approach

Using the renormalization-group approach, we consider an analytic theory describing the formation of a self-focusing structure of a laser beam in a plasma with relativistic nonlinearity for a given radial intensity distribution at the entrance and derive approximate analytic solutions. We study three stationary self-focused waveguide propagation modes with respect to controlling laser-plasma parameters for a Gaussian radial intensity distribution at the plasma boundary. The proposed theory specifies the domains and their boundaries on the plane of the controlling parameters where (1) self-trapping, (2) self-focusing on the axis, and (3) tubular self-focusing solutions occur. We review the concept of the critical power and show that it must be correlated to the form of the entering light pulse and its value corresponding to the minimum power that admits self-channeling can be significantly lower than the widely used value 17(ω^{2}/ω_{pe}^{2}) GW.

Controlling multiple filaments by relativistic optical vortex beams in plasmas

Filamentation dynamics of relativistic optical vortex beams (OVBs) propagating in underdense plasma is investigated. It is shown that OVBs with finite orbital angular momentum (OAM) exhibit much more robust propagation behavior than the standard Gaussian beam. In fact, the growth rate of the azimuthal modulational instability decreases rapidly with increase of the OVB topological charge. Thus, relativistic OVBs can maintain their profiles for significantly longer distances in an underdense plasma before filamentation occurs. It is also found that an OVB would then break up into regular filament patterns due to conservation of the OAM, in contrast to a Gaussian laser beam, which in general experiences random filamentation.

Rewriting the rules governing high intensity interactions of light with matter

The trajectory of discovery associated with the study of high-intensity nonlinear radiative interactions with matter and corresponding nonlinear modes of electromagnetic propagation through material that have been conducted over the last 50 years can be presented as a landscape in the intensity/quantum energy [I-ħω] plane. Based on an extensive series of experimental and theoretical findings, a universal zone of anomalous enhanced electromagnetic coupling, designated as the fundamental nonlinear domain, can be defined. Since the lower boundaries of this region for all atomic matter correspond to ħω ~ 10(3) eV and I  ≈  10(16) W cm(-2), it heralds a future dominated by x-ray and γ-ray studies of all phases of matter including nuclear states. The augmented strength of the interaction with materials can be generally expressed as an increase in the basic electromagnetic coupling constant in which the fine structure constant α  →  Z(2)α, where Z denotes the number of electrons participating in an ordered response to the driving field. Since radiative conditions strongly favoring the development of this enhanced electromagnetic coupling are readily produced in self-trapped plasma channels, the processes associated with the generation of nonlinear interactions with materials stand in natural alliance with the nonlinear mechanisms that induce confined propagation. An experimental example involving the Xe (4d(10)5s(2)5p(6)) supershell for which Z  ≅  18 that falls in the specified anomalous nonlinear domain is described. This yields an effective coupling constant of Z(2)α  ≅  2.4  >  1, a magnitude comparable to the strong interaction and a value rendering as useless conventional perturbative analyses founded on an expansion in powers of α. This enhancement can be quantitatively understood as a direct consequence of the dominant role played by coherently driven multiply-excited states in the dynamics of the coupling. It is also conclusively demonstrated by an abundance of data that the utterly peerless champion of the experimental campaign leading to the definition of the fundamental nonlinear domain was excimer laser technology. The basis of this unique role was the ability to satisfy simultaneously a triplet (ω, I, P) of conditions stating the minimal values of the frequency ω, intensity I, and the power P necessary to enable the key physical processes to be experimentally observed and controllably combined. The historical confluence of these developments creates a solid foundation for the prediction of future advances in the fundamental understanding of ultra-high power density states of matter. The atomic findings graciously generalize to the composition of a nuclear stanza expressing the accessibility of the nuclear domain. With this basis serving as the launch platform, a cadenza of three grand challenge problems representing both new materials and new interactions is presented for future solution; they are (1) the performance of an experimental probe of the properties of the vacuum state associated with the dark energy at an intensity approaching the Schwinger/Heisenberg limit, (2) the attainment of amplification in the γ-ray region (~1 MeV) and the discovery of a nuclear excimer, and (3) the determination of a path to the projected super-heavy nuclear island of stability.

Mitigating the relativistic laser beam filamentation via an elliptical beam profile

It is shown that the filamentation instability of relativistically intense laser pulses in plasmas can be mitigated in the case where the laser beam has an elliptically distributed beam profile. A high-power elliptical Gaussian laser beam would break up into a regular filamentation pattern-in contrast to the randomly distributed filaments of a circularly distributed laser beam-and much more laser power would be concentrated in the central region. A highly elliptically distributed laser beam experiences anisotropic self-focusing and diffraction processes in the plasma channel ensuring that the unstable diffractive rings of the circular case cannot be produced. The azimuthal modulational instability is thereby suppressed. These findings are verified by three-dimensional particle-in-cell simulations.

Controlling the length of plasma waveguide up to 5 mm, produced by femtosecond laser pulses in atomic clustered gas

We report the observation of longitudinally uniform plasma waveguide with a controlled length of up to nearly 5 mm, in argon clustered gas jet. This self-channeling plasma is obtained using a 35 mJ, 30 fs FWHM pulse as a pump laser pulse to create the plasma channel. A 1 mJ pulse of the same laser is used for probing the plasma channels using interferometric diagnostics. The radial distribution of the electron density confirms the formation of a plasma waveguide. Clustered argon enhances the absorption efficiency of femtosecond pulses which enables the use of pump pulses of only 35 mJ, approximately 10 times less energy than required for heating conventional gas targets. The plasma channel length is controlled by the laser focus point (F), the laser intensity (I), the pump-probe delay time (t) and the laser height from a nozzle (z). The variation of the electron density for these parameters is also studied. We found that the highest density of 1.2 x 10(19) cm(-3) was obtained at I = 5.2 x 10(16) W/cm(2), z = 2 mm and t = 7.6 ns. It was demonstrated that by using a clustered jet, both the plasma waveguide length and the plasma density could be controlled.

Modeling of clusters in a strong 248-nm laser field by a three-dimensional relativistic molecular dynamic model

A relativistic time-dependent three-dimensional particle simulation model has been developed to study the interaction of intense ultrashort KrF (248 nm) laser pulses with small Xe clusters. The trajectories of the electrons and ions are treated classically according to the relativistic equation of motion. The model has been applied to a different regime of ultrahigh intensities extending to 10(21) W/ cm(2). In particular, the behavior of the interaction with the clusters from intensities of approximately 10(15) W/cm(2) to intensities sufficient for a transition to the so-called "collective oscillation model" has been explored. At peak intensities below 10(20) W/cm(2), all electrons are removed from the cluster and form a plasma. It is found that the "collective oscillation model" commences at intensities in excess of 10(20) W/cm(2), the range that can be reached in stable relativistic channels. At these high intensities, the magnetic field has a profound effect on the shape and trajectory of the electron cloud. Specifically, the electrons are accelerated to relativistic velocities with energies exceeding 1 MeV in the direction of laser propagation and the magnetic field distorts the shape of the electron cloud to give the form of a pancake.

Optimization of power compression and stability of relativistic and ponderomotive self-channeling of 248 nm laser pulses in underdense plasmas

The controlled formation in an underdense plasma of stable multi-PW relativistic micrometer-scale channels, which conduct a confined power at 248 nm exceeding 10(4) critical powers and establish a peak channel intensity of approximately 10(23) W/ cm(2) , can be achieved with the use of an appropriate gradient in the electron density in the initial launching phase of the confined propagation. This mode of channel formation optimizes both the power compression and the stability by smoothing the transition from the incident spatial profile to that associated with the lowest channel eigenmode, the dynamically robust structure that governs the confined propagation. A chief outcome is the ability to stably conduct coherent energy at fluences greater than 10(9) J/ cm(2) .

Interactive dynamics of two copropagating laser beams in underdense plasmas

The interaction of two copropagating laser beams with crossed polarization in the underdense plasmas has been investigated analytically with the variational approach and numerically. The coupled envelope equations of the two beams include both the relativistic mass correction and the ponderomotive force effect. It is found that the relativistic effect always plays the role of beam attraction, while the ponderomotive force can play both the beam attraction and beam repulsion, depending upon the beam diameters and their transverse separation. In certain conditions, the two beam centers oscillate transversely around a propagation axis. In this case, the ponderomotive effect can lead to a higher oscillation frequency than that accounting for the relativistic effect only. The interaction of two beams decreases the threshold power for self-focusing of the single beam. A strong self-trapping beam can channel a weak one.

Laser self-focusing in the presence of quasistatic axial direct current

We try to understand the presence of a quasistatic magnetic field on the basis of the stability of the laser-plasma system. A general theoretical model of laser self-focusing in the absence of a quasistatic magnetic field (QMF) is extended to discuss self-focusing in the presence of a QMF. Various transverse intensity profiles under different axial collective electronic speeds V(z) are calculated. Numerical results indicate that for suitable laser power and plasma density, the increment in V(z) can lead to a further separation between the photon fluid and the electron fluid and hence a decrement in the energy of the laser-plasma system. This causes it to be possible for the system state without a QMF, or V(z) =0 state, to be not stable relative to some V(z) not equal 0 states.

Isolated attosecond pulses generated by relativistic effects in a wavelength-cubed focal volume

Lasers that provide an energy encompassed in a focal volume of a few cubic wavelengths (lambda3) can create relativistic intensity with maximal gradients using minimal energy. With particle-in-cell simulations we found that single 200-as pulses could be produced efficiently in a lambda3 laser pulse reflection by means of deflection and phase compression caused by the coherent motion of the plasma electrons that emit these pulses. This novel technique is efficient (approximately 10%) and can produce single attosecond pulses from the millijoule to the joule level.

Relativistic generation of isolated attosecond pulses in a lambda 3 focal volume

Lasers that provide an energy encompassed in a focal volume of a few cubic wavelengths (lambda(3)) can create relativistic intensity with maximal gradients, using minimal energy. With particle-in-cell simulations we found, that single 200 attosecond pulses could be produced efficiently in a lambda(3) laser pulse reflection, via deflection and compression from the relativistic plasma mirror created by the pulse itself. An analytical model of coherent radiation from a charged layer confirms the pulse compression and is in good agreement with simulations. The novel technique is efficient (approximately 10%) and can produce single attosecond pulses from the millijoule to the joule level.

Effect of a laser prepulse on a narrow-cone ejection of MeV electrons from a gas jet irradiated by an ultrashort laser pulse

Spatial and energy distributions of energetic electrons produced by an ultrashort, intense laser pulse with a short focal length optical system (Ti:sapphire, 12 TW, 50 fs, lambda=790 nm, f/3.5) in a He gas jet are measured. They are shown to depend strongly on the contrast ratio and shape of the laser prepulse. The wave breaking of the plasma waves at the front of the shock wave formed by a proper laser prepulse is found to make a narrow-cone (0.1pi mm mrad) electron injection. These electrons are further accelerated by the plasma wake field generated by the laser pulse up to tens of MeV forming a Maxwell-like energy distribution. In the case of nonmonotonic prepulse, hydrodynamic instability at the shock front leads to a broader, spotted spatial distribution. The numerical analysis based on a two-dimensional (2D) hydrodynamic (for the laser prepulse) and 2D particle-in-cell (PIC) simulation justifies the mechanism of electron acceleration. The PIC calculation predicts that electrons with energy from 10 to 40 MeV form a bunch with a pulse duration of about 40 fs.

Axial magnetic fields in relativistic self-focusing channels

Based on an improved cavitation model for the electron dynamics, an exact analysis is presented of the generation of axial magnetic fields in the relativistic self-focusing channels produced by circularly polarized light in plasmas. Two kinds of waveguiding structures are considered: single-channel waveguides and plasma filaments surrounded by a light field. It is found that due to large electron density gradients in the cavitation plasma, magnetic fields of megagauss values with opposite directions separated by a neutral sheet, where the magnetic field passes through zero, can be produced.

Self-focusing and merging of two copropagating laser beams in underdense plasma

The propagation of two laser beams copropagating in underdense plasma has been studied numerically by solving their coupled envelope equations. It shows that two beams can merge each other, or split into three beams, or propagate with unstable trajectories, depending upon their power and initial beam separation. During the merging process, strong emission of radiation is observed. It also shows that the density cavitation channels due to the transverse ponderomotive force of the beams tend to trap them inside and prevent them from merging each other.

Propagation of short intense laser pulses in gas-filled capillaries

The guided laser pulse propagation and wake-field generation are studied in a wide (in comparison with the laser spot size) gas-filled capillary with an on-axis gas density depletion, which can be produced by a rapid spin of the capillary around its axis or by radially propagating shock waves generated in a piezoceramic tube. A single equation for the wake-field potential, which describes the fully relativistic plasma response in the presence of optical field ionization (OFI) of a gas, is derived and used to demonstrate a guided propagation of a short intense laser pulse over many Rayleigh lengths in a leaky plasma channel produced by the pulse due to OFI in the capillary filled with a radially inhomogeneous gas. The efficient generation of a regular wake field over long distances suitable for the laser wake-field accelerators is shown.

Dynamics of self-trapped singular beams in an underdense plasma

Dynamics of an intense short laser pulse with a phase singularity, propagating in an underdense cold plasma, is investigated. Such a pulse can propagate as a vortex soliton in a self-created channel. It is shown that vortices with the topological charge m=1,2 (and a corresponding angular momentum) are unstable against symmetry-breaking perturbations; the breakup of the original vortex leads to the formation of stable spatial solitons that steadily fly away tangentially from the initial ring of vortex distribution.

Polarization effects and anisotropy in three-dimensional relativistic self-focusing

The relativistic self-focusing of high-intensity laser pulses in underdense plasmas is investigated with three-dimensional particle in cell simulations. The different behavior of a linearly polarized pulse in the two transverse directions is interpreted as a combination of two two-dimensional responses with different polarizations. In the polarization plane a high density sheet is formed, which separates the two regions of oppositely directed quasistatic magnetic field.

Harmonic generation of ultraintense laser pulses in underdense plasma

We propose a nonlinear theory of the generation of harmonic radiation from the interaction of ultraintense laser beams with plasma. The harmonic generation is related to the transition of the laser-plasma equilibrium state. By taking into account correlations among sidebands, we study many sidebands comprehensively. The harmonic generation is viewed as a redistribution of laser field over different frequencies because of the requirement of system stability. We introduce a system parameter S that is related to the sideband intensity spectrum and self-consistently calculate the value of S. Our numerical experiments reveal that the variations of controllable system parameters, plasma density, and laser peak intensity have a great effect on S.

Axisymmetric relativistic self-channeling of laser light in plasmas

By using an improved cavitation model, relativistic self-channeling structures are derived, which make it possible to propagate laser powers exceeding the critical one for self-focusing. A propagation mode for high laser power is also presented which is qualitatively different from those in the weakly relativistic case. Structural stability analysis shows that stable self-wave-guide propagation can take place.

Self-magnetized effects in relativistic cold plasmas due to ponderomotive forces: application to relativistic magnetic guiding of light

Nonlinear equations are derived relevant to describe the propagation of powerful electromagnetic fields launched within a plasma. The nonlinear generation of self-induced collective electromagnetic perturbations are obtained with matter lying in the relativistic regime. Our main result is the self-consistent treatment of the coupled equations between the pump and its self-induced fields. In particular, a mechanism is pointed out for self-generation of quasistatic magnetic field that is due to the relativistic ponderomotive force. This process is found to be more efficient to produce quasistatic magnetic fields, as confirmed by recent experiments, as compared to known effects such as the inverse Faraday effect. As an application, we investigate conditions for relativistic magnetic guiding of light to occur under the combined action of the self-induced density and magnetic field.

Electromagnetic energy penetration in the self-induced transparency regime of relativistic laser-plasma interactions

Two qualitatively different scenarios for the penetration of relativistically intense laser radiation into an overdense plasma, accessible by self-induced transparency, are presented. In the first one, penetration of laser energy occurs by solitonlike structures moving into the plasma. This scenario occurs at plasma densities less than approximately 1.5 times the critical one (depending on ion mass). At higher background densities, laser light penetrates only over a finite length which increases with incident intensity. In this regime the plasma-field structures represent alternating electron (and, on longer time scales, ion) layers separated by about half a wavelength of cavitation with concomitant strong charge separation.

Anisotropic filamentation instability of intense laser beams in plasmas near the critical density

The relativistic filamentation instability (RFI) of linearly polarized intense laser beams in plasmas near the critical density is investigated. It is found that the RFI is anisotropic to transverse perturbations in this case; a homogeneous laser beam evolves to a stratified structure parallel to the laser polarization direction, as demonstrated recently with three-dimensional particle-in-cell simulations by Nishihara et al. [Proc. SPIE 3886, 90 (2000)]. A weakly relativistic theory is developed for plasmas near the critical density. It shows that the anisotropy of the RFI results from a suppression of the instability in the laser polarization direction due to the electrostatic response. The anisotropic RFI is also analyzed based on an envelope equation for the laser beam. Finally, the envelope equation is solved numerically, and anisotropic filamentation and self-focusing are illustrated.

Multifilament structures in relativistic self-focusing

A simple model is derived to prove the multifilament structure of relativistic self-focusing with ultraintense lasers. Exact analytical solutions describing the transverse structure of waveguide channels with electron cavitation, for which both the relativistic and ponderomotive nonlinearities are taken into account, are presented.

Nonlinear propagation of short intense laser pulses in a hollow metallic waveguide

The propagation of a short intense laser pulse in the femtosecond range in a hollow metallic waveguide gives rise to heating of the metallic wall. The temperature of the degenerate electron gas in the wall is increased during the pulse duration and this heating affects the propagation and dissipation of the laser pulse. Analytical and numerical analysis shows that, as the dissipation is increased, the leading edge of the pulse decreases more slowly than the rear, resulting in a pulse shortening.

Wakefield generation and GeV acceleration in tapered plasma channels

To achieve multi-GeV electron energies in the laser wakefield accelerator (LWFA), it is necessary to propagate an intense laser pulse long distances in a plasma without disruption. One of the purposes of this paper is to evaluate the stability properties of intense laser pulses propagating extended distances (many tens of Rayleigh ranges) in plasma channels. A three-dimensional envelope equation for the laser field is derived that includes nonparaxial effects such as group velocity dispersion, as well as wakefield and relativistic nonlinearities. It is shown that in the broad beam, short pulse limit the nonlinear terms in the wave equation that lead to Raman and modulation instabilities cancel. This cancellation can result in pulse propagation over extended distances, limited only by dispersion. Since relativistic focusing is not effective for short pulses, the plasma channel provides the guiding necessary for long distance propagation. Long pulses (greater than several plasma wavelengths), on the other hand, experience substantial modification due to Raman and modulation instabilities. For both short and long pulses the seed for instability growth is inherently determined by the pulse shape and not by background noise. These results would indicate that the self-modulated LWFA is not the optimal configuration for achieving high energies. The standard LWFA, although having smaller accelerating fields, can provide acceleration for longer distances. It is shown that by increasing the plasma density as a function of distance, the phase velocity of the accelerating field behind the laser pulse can be made equal to the speed of light. Thus electron dephasing in the accelerating wakefield can be avoided and energy gain increased by spatially tapering the plasma channel. Depending on the tapering gradient, this luminous wakefield phase velocity is obtained several plasma wavelengths behind the laser pulse. Simulations of laser pulses propagating in a tapered plasma channel are presented. Experimental techniques for generating a tapered density in a capillary discharge are described and an example of a GeV channel guided standard LWFA is presented.

Stable laser-pulse propagation in plasma channels for GeV electron acceleration

To achieve multi-GeV electron energies in the laser wakefield accelerator (LWFA) it is necessary to propagate an intense laser pulse long distances in plasma without disruption. A 3D envelope equation for a laser pulse in a tapered plasma channel is derived, which includes wakefields and relativistic and nonparaxial effects, such as finite pulse length and group velocity dispersion. It is shown that electron energies of approximately GeV in a plasma-channel LWFA can be achieved by using short pulses where the forward Raman and modulation nonlinearities tend to cancel. Further energy gain can be achieved by tapering the plasma density to reduce electron dephasing.

Structure stability of ultraintense laser pulse in transverse homogeneous cold plasma

We study transverse structure symmetry of an ultraintense laser pulse through transverse homogeneous cold plasma. We derive a steady-structure equation of laser pulse and solve it under different on-axis conditions. We compare Hamiltonian values at solutions with different on-axis conditions to examine their relative stability. Numerical results show that for different ionic density, symmetric structure is not always stable relative to asymmetric one of same power. For a given ionic density, whether a symmetric structure is stable is determined by its power. This result agrees with the phenomenon of pulse "head bending", qualitatively. Our theory reveals that, in addition to the plasma's transverse inhomogeneity, there is another mechanism responsible for asymmetric structure.

Relativistic focusing and ponderomotive channeling of intense laser beams

The ponderomotive force associated with an intense laser beam expels electrons radially and can lead to cavitation in plasma. Relativistic effects as well as ponderomotive expulsion of electrons modify the refractive index. An envelope equation for the laser spot size is derived, using the source-dependent expansion method with Laguerre-Gaussian eigenfunctions, and reduced to quadrature. The envelope equation is valid for arbitrary laser intensity within the long pulse, quasistatic approximation and neglects instabilities. Solutions of the envelope equation are discussed in terms of an effective potential for the laser spot size. An analytical expression for the effective potential is given. For laser powers exceeding the critical power for relativistic self-focusing the analysis indicates that a significant contraction of the spot size and a corresponding increase in intensity is possible.

Laser pulse modulation instabilities in plasma channels

In this paper the modulational instability associated with propagation of intense laser pulses in a partially stripped, preformed plasma channel is analyzed. In general, modulation instabilities are caused by the interplay between (anomalous) group velocity dispersion and self-phase modulation. The analysis is based on a systematic approach that includes finite-perturbation-length effects, nonlinearities, group velocity dispersion, and transverse effects. To properly include the radial variation of both the laser field and plasma channel, the source-dependent expansion method for analyzing the wave equation is employed. Matched equilibria for a laser beam propagating in a plasma channel are obtained and analyzed. Modulation of a uniform (matched) laser beam equilibrium in a plasma channel leads to a coupled pair of differential equations for the perturbed spot size and laser field amplitude. A general dispersion relation is derived and solved. Surface plots of the spatial growth rate as a function of laser beam power and the modulation wave number are presented.

Long-scale jet formation with specularly reflected light in ultraintense laser-plasma interactions

Long-scale jetlike x-ray emission was observed in a 100-TW laser-plasma interaction. The jet was well collimated with a divergence of 30-40 mrad and continued from the target surface into underdense regions for a distance over 4 mm in the specular direction of the laser light. A two-dimensional particle-in-cell simulation shows an electron acceleration with the specularly reflected laser light and collimation of the electron stream by a self-generated magnetic field, resulting in the electron jet to the direction of the specularly reflected light.

Acceleration and double-peak spectrum of hot electrons in relativistic laser plasmas

A spectrum equation of hot electrons in relativistic laser plasmas is derived in which two hot-electron population peaks appear as the laser strength parameter reaches a threshold. These calculations can explain the generation of very hot electrons with several tens of MeV energy and two hot-electron population peaks observed in the recent experiments.

Formation of plasma channels in the interaction of a nanosecond laser pulse at moderate intensities with helium gas jets

We report on a detailed study of channel formation in the interaction of a nanosecond laser pulse with a He gas jet. A complete set of diagnostics is used in order to characterize the plasma precisely. The evolution of the plasma radius and of the electron density and temperature are measured by Thomson scattering, Schlieren imaging, and Mach-Zehnder interferometry. In gas jets, one observes the formation of a channel with a deep density depletion on axis. Because of ionization-induced defocusing which increases the size of the focal spot and decreases the maximum laser intensity, no channel is observed in the case of a gas-filled chamber. The results obtained in various gas-jet and laser conditions show that the channel radius, as well as the density along the propagation axis, can be adjusted by changing the laser energy and gas-jet pressure. This is a crucial issue when one wants to adapt the channel parameters in order to guide a subsequent high-intensity laser pulse. The experimental results and their comparison with one-dimensional (1D) and two-dimensional hydrodynamic simulations show that the main mechanism for channel formation is the hydrodynamic evolution behind a supersonic electron heat wave propagating radially in the plasma. It is also shown from 2D simulations that a fraction of the long pulse can be self-guided in the channel it creates. The preliminary results and analyses on this subject have been published before [V. Malka et al., Phys. Rev. Lett. 79, 2979 (1997)].

Stable relativistic/charge-displacement channels in ultrahigh power density (approximately 10(21 W/cm3) plasmas

Robust stability is a chief characteristic of relativistic/charge-displacement self-channeling. Theoretical analysis of the dynamics of this stability (i) reveals a leading role for the eigenmodes in the development of stable channels, (ii) suggests a technique using a simple longitudinal gradient in the electron density to extend the zone of stability into the high electron density/high power density regime, (iii) indicates that a situation approaching unconditional stability can be achieved, (iv) demonstrates the efficacy of the stable dynamics in trapping severely perturbed beams in single uniform channels, and (v) predicts that approximately 10(4) critical powers can be trapped in a single stable channel. The scaling of the maximum power density with the propagating wavelength lambda is shown to be proportional to lambda-4 for a given propagating power and a fixed ratio of the electron plasma density to the critical plasma density. An estimate of the maximum power density that can be achieved in these channels with a power of approximately 2 TW at a UV (248 nm) wavelength gives a value of approximately 10(21) W/cm3 with a corresponding atomic specific magnitude of approximately 60 W/atom. The characteristic intensity propagating in the channel under these conditions exceeds 10(21) W/cm2.

Nonlinear Optics in Relativistic Plasmas and Laser Wake Field Acceleration of Electrons

When a terawatt-peak-power laser beam is focused into a gas jet, an electron plasma wave, driven by forward Raman scattering, is observed to accelerate a naturally collimated beam of electrons to relativistic energies (up to 10(9) total electrons, with an energy distribution maximizing at 2 megaelectron volts, a transverse emittance as low as 1 millimeter-milliradian, and a field gradient of up to 2 gigaelectron volts per centimeter). Electron acceleration and the appearance of high-frequency modulations in the transmitted light spectrum were both found to have sharp thresholds in laser power and plasma density. A hole in the center of the electron beam may indicate that plasma electrons were expelled radially.